Research On Meshing Theory Of Archimedes Conical Worm Pair

In this paper,the meshing principle of the Archimedes conical worm pair is taken as the research object.With a conical reference surface,the worm’s mating member is a face-type gear.The worm pair is a line contact meshing transmission with concave and convex arc tooth profiles,so it has the characteristics of small contact stress,high precision,large bearing capacity and compact structure.The helicoidal surface of the worm is finish-turned by a lathe tool with straight blade,thus the tooth profile of worm in the axial section is straight line.The teeth of the mating gear may be machined by a conical hobber,whose generating surface is completely identical to the helicoid of the mating worm.From its forming principle,the helicoid of the worm is Archimedes helicoid,and that’s where its name,Archimedes conic worm drive,came from.Besides,this paper establishes the mathematical model of the Archimedes conical worm pair in its meshing process,and conducts research on its meshing theory as follows:(1)The equation of the Archimedes conical worm is established based on its forming principle.At first,the properties of its helicoid are specifically analyzed.In addition,the equation of the worm is deduced by means of the spherical vector coordinates.By utilizing the knowledge of differential geometry,the unit normal vector,two basic quantities as well as the curvature parameters of the helicoid are calculated(2)The meshing principle of the Archimedes conical worm drive based on the tooth surface equation is studied.The relative coordinate system of the process of machining worm is established in accordance with the relative position of the worm pair.According to the differential geometry and the gear meshing theory,the meshing function and two kinds of boundary functions of the worm pair are deduced,moreover,two meshing performance parameters which indicate its local meshing characteristics are further calculated.Then the tooth surface equation of the worm gear is deduced by means of the relative position of the worm pair and coordinate transformation.Moreover,the boundary equation of the worm pair used to determinate the conjugate region is established by utilizing the knowledge of reference point.At last,an approach based on the theory regarding algebraic equation of higher degree is put forth to compute the meshing limit line for a conical worm drive,which needs no iteration to be performed and simplifies the corresponding computer program.(3)The meshing principle of the Archimedes conical worm drive based on the reference point is studied.By means of reference point which is determined by the tooth surface equation,a pair of reference cones are established.In addition,the expressions for calculating the basic parameters of the worm pair are derived,meanwhile,their precision is verified.At last,a new calculation method which is applicable to the Archimedes conical worm drive and relies on the unit normal vector to compute the pressure angle of the helicoid is proposed.Moreover,this method is utilized to recalculate the meshing performance parameters of any single point on the tooth surface.(4)The numerical simulation and analysis of the Archimedes conical worm drive are carried out.Firstly,the curvature interference boundary line of the worm pair is determined and drawn,the corresponding theoretical and numerical analysis is conducted.Accordingly,a valid matching principle of parameters is put forward.At the same time,the conjugate region on the tooth surface of worm pair is established.Then,each contacting point of instantaneous contact line on conjugate region are determined respectively,whose meshing performance parameters are also calculated.Therefore,the regularity of influence of process parameters on the meshing performance of worm pair is explored.